Letter pubs.acs.org/JPCL
p−n Junction at the Interface between Metallic Systems Gustavo Ramírez-Caballero,† Julibeth M. Martínez de la Hoz, and Perla B. Balbuena* Department of Chemical Engineering and Materials Science and Engineering Program, Texas A&M University, College Station, Texas 77843, United States ABSTRACT: Density functional theory is used to evaluate the electronic properties in a composite metallic material consisting of two subsystems made of interacting metallic thin films separated by a subnanometer gap. One of the subsystems, M/Pt-M/Pt, has a monolayer of metal M over a core of Pt atoms, and the other is Pt−Pt, where the interacting surfaces are made of pure Pt. At equilibrium, this composite material exhibits a potential barrier at the interface, resembling a semiconductor p−n junction. In the gap region of M/Pt−M/Pt, the amount of electrons correlates with the surface layer degree of polarization, which depends on electronegativity and number of unpaired electrons in the external shells. The electron density in the gap, the system work function, and the built-in potential at the interface of the composite system calculated for various metal skins correlate with the degree of reduction of the Pt atoms located at the junction area. SECTION: Surfaces, Interfaces, Catalysis
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nteractions between metallic surfaces separated at subnanometer distances induce interesting physicochemical phenomena such as molecular dissociation,1,2 molecular transformation into anion species,3 and magnetic effects.4 Unusual chemistry may take place, leading to lower activation energies5 and/or new reaction pathways.6−9 Here we explore other fundamental features of the same phenomena, which may lead to further developments and applications in diverse areas including catalysis, electrochemistry, sensors, and electronics. Engineering materials usually refer to tailoring synthetic materials with specific or novel physical, mechanical, and chemical properties. Most of the devices based on semiconductor nanostructures are engineered materials. Among them, p−n junctions play an important role as elementary building blocks. Several semiconductor devices such as transistors, diodes, light-emitting diodes (LEDs), integrated circuits, and solar cells are based on p−n junctions. The physical properties of p−n junctions are based on the formation of a potential barrier across the junction in an equilibrium state of the material. In this work, we evaluate a composite metallic system having a potential barrier at equilibrium that resembles a semiconductor p−n junction. The composite metallic system results from the combination of two subsystems: each subsystem consists of two interacting thin films separated by a 4−10 Å gap. The first subsystem (Figure 1, left side) is formed by interacting skin−metal M/Pt surfaces composed of a core of Pt atoms and a single overlayer of a different metal, M. The second subsystem (Figure 1, right side) is composed only of Pt atoms. The two subsystems form the composite material that displays features of a p−n junction in the y direction. The proposed composite system has two characteristics that may play an important role in the continuous race for downscaling of solid state devices: one refers to the basic © 2012 American Chemical Society
Figure 1. Interface formed by the junction of M/Pt−M/Pt and Pt−Pt subsystems. The M/Pt system consists in monolayer metal M, (M = Ti, V, Fe, Co, Ni, Cu, Tc, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, and Au) sitting on a substrate of different chemical nature, in this case pure Pt. The periodicity of the slab model in the z directions allows the separation between slabs, here of 5 Å, and the formation of a gap between films.
physical phenomena occurring in the material, and the second refers to the specific materials that compose the system allowing tunability of the desired effects. The physical phenomena are associated with quantum tunneling, which may result in a disadvantage or advantage for downscaling of electronic devices. Disadvantage occurs in applications in which Received: January 15, 2012 Accepted: March 4, 2012 Published: March 4, 2012 818
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Figure 2. Nonuniform distribution of the electron density along the gap between metallic thin film surfaces; the separation between the thin films is 5 Å. The nonuniform electron density distribution is due to the interfacial structure composed by a region delimited by Ti/Pt interacting skin surfaces in contact with another region defined by interacting pure Pt surfaces. The purple region has the highest electron density, and it decreases through the blue, green, yellow, and red.
function of the system, and potential barrier at the junction interface for various metal skin surfaces. The dependence of these variables on the nature of the metal skin is then correlated with the location of the metal skin in the periodic table. The results are discussed in order to present a possible explanation of the process of forming a built-in potential characteristic of a p−n junction. Electron Density in the Gap and Charge Transfer at the Interface.Figure 2 represents a composite system formed by a Ti/Pt−Ti Pt subsystem in contact in the y direction with a second Pt−Pt subsystem. The surface−surface separation in both subsystems is 5 Å. It was found that the electron density generated in the gap between the surfaces is different in each region of the system: there is a higher electron density in the region of Ti/Pt−Ti/Pt than in the pure Pt region due to the different chemical nature of the Ti surface. This difference in electron density between the two regions is expected to generate electrostatic and energetic phenomena that can be calculated. We illustrate this point by evaluation of the electron density in the gap, work function of the system, electrostatic potential, and net charge transfer at the interface. Figure 3 shows the net charge in the surface atoms for the individual subsystems Ti/Pt−Ti/Pt and Pt−Pt, and for the composite system. A reduction−oxidation reaction takes place between the surface monolayer and the subsurface layer, which is reflected in the Ti/Pt skin system (case a) as a positive charge (0.48), indicating that Ti atoms lose electrons gained by Pt atoms. For pure Pt (case b), a slightly negative charge borne by the surface atoms indicates that there is a small electron gain from the top layer atoms as a consequence of their low coordination number with respect to the bulk atoms. In the composite system (case c), the net charges of the surface atoms at the interface between the two systems are significantly different from those of the individual systems (d and e), revealing a much higher electron transfer between Ti that loses electrons to Pt, which gains electrons. Ef fect of the Nature of the Overlayer Metal M in M/Pt−M/Pt Systems. Different metal skin−surfaces (M/Pt) were studied to determine the equilibrium amount of electrons in the gap between thin films and the minimum energy needed to remove
electron leakage is deleterious such as the case of complementary metal-oxide semiconductor (CMOS) transistors, which, at the limit of a five-layer thick oxide, results in a high leakage gate current due to tunneling effects from the gate into the film. Advantages in downscaling are expected for devices such as the tunnel diode and single-electron transistors, where quantum tunneling is the electron transfer mechanism. Since the scale at which quantum tunneling occurs is on the order of a few angstroms, it seems like quantum tunneling is a key phenomenon of the electron transfer mechanism suitable for the downscale of integrated circuits.10 In the same downscale paradigm, most electronic devices may approach fundamental limits with the present pattern transfer technique, photolithography.11 This fundamental limitation urges the development of devices based on new materials. Metals can be an alternative, since in general they outperform silicon-based materials due to their significantly higher conductivities, less short channel restrictions, and single-step lithography process. The literature and technological applications of the concept of electron tunneling are abundant, and it is an active field in today’s research activities. An early start was the idea of using Coulomb charging effects that appear due to the localization of individual electrons in islands between tunnel junctions for performing electronic functions at immensely higher densities. Likharev proposed transistors by controlling the tunneling of electrons across double junction series by an applied bias,12 which was soon demonstrated by Dolan et al.13 This finding motivated the design of digital logic circuits in double-junctions using the Coulomb blockade effect, which is the block of all tunnel events near zero bias voltage in series arrays of junctions.14 This kind of transistor is called a single-electron transistor (SET), the most studied device in the field of single charge electronics. In the fabrication of SET, metals form two small tunnel junctions connected in series that compose the transistor.15 In addition to SET, other kind of metallic transistor has been proposed that uses the electric field effects on metallic nanotubes and planar metallic nanowire structures.16,17 Here we use density functional theory (DFT) to evaluate the electron density in the gap between thin films (Figure 1), work 819
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Figure 3. Sketch of systems: (a) Ti/Pt; (b) pure Pt, and (c) composite Ti/Pt-pure Pt. Charge in each surface and subsurface atom: (d) Ti/Pt; (e) pure Pt, and (f) composite Ti/Pt-pure Pt. For the composite system there is a charge transfer at the interface, as illustrated in case f. Compared to the charges in d and e, there is a negligible change in the charge of the subsurface atoms after forming the interface, with the exception of the Pt atoms just below the junction that bear −0.12e.
atom, with positive values indicating oxidation. The general trend, with the exception of Ag and Au in the fifth and sixth periods, is that the number of electrons in the gap increases with the oxidation of the surface overlayer atoms, and correlates with the decrease of the work function, especially for the fourth and sixth periods. The average work function for systems of skin atoms pertaining to the same period in the periodic table was found to be a function of the period 4.59 eV for n = 4, 5.12 eV for n = 5, and 5.47 eV for n = 6. There is also a trend with respect to the period: the work function increases as the period n increases. The exceptions of the just described general trends are for transition metals belonging to group 11: Cu, Ag, and Au. This out-of-trend behavior may be related with the fact that the outermost d orbital of these metals is full with its 10 electrons, and therefore these atoms are less prone to act as electron donors.
an electron from the material or work function of the system, as shown in Table 1. Table 1 indicates that the amount of electrons in the gap between metallic thin films and the work function of the system can be tuned by changing the nature of the metallic skin layer. On the other hand, the work function of each skin−surface system in Table 1 is smaller than that of pure Pt, therefore the studied skin systems would be prone to transfer electrons to the Pt side. The results in Table 1 may be arranged with respect to the position of the overlayer metal M in the periodic table, namely, metals belonging to the fourth, fifth, and sixth periods, as shown in Figure 4. The trends indicate that the amount of electrons in the gap increases as the atomic number decreases in a given period. The number of electrons in the gap and work function are correlated in each period with the charge gained or lost by the surface overlayer atoms due to the interaction with the Pt subsurface atoms; the charge reported in Figure 4 is per 820
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On the other hand, for a given group in the periodic table, as n increases, the electronegativity decreases, and the average number of electrons in the gap increases. Since the electronegativity is related to the definition of work function in solids, the concept supports the general trends presented in Figure 4. Furthermore, the number of electrons in the gap could be related to the number of unpaired electrons in the most external orbitals: the higher the number of unpaired electrons, the higher the mobility of electrons, the easier the electron migration to fill the gap, and thus the higher the number of electrons in the gap. Indeed, Figure 4 illustrates that for a given period, the number of electrons in the gap increases with the number of unpaired electrons as Z decreases. Composite M/Pt−Pt Slab Systems. By putting together M/Pt− M/Pt and Pt−Pt subsystems, the electrons in the system flow to new locations until an equilibrium is reached in which the Fermi energy, and therefore the chemical potential, are equal at both sides of the interface. Most of the transfer of electrons necessary to reach equilibrium in the system occurs between the atoms located at the interface; in the case shown in Figure 3c, a large part of the charge transfer occurs between Ti and Pt surface atoms at the interface. At equilibrium, the electronic density in the gap is different in each region and, as a consequence, a potential barrier is formed in the gap, at the junction region between the metal thin films in contact, as shown in Figure 5. In the gap between metallic thin films, at the junction point, a built-in potential results in the y direction. Figure 6 shows an illustration of the electrostatic potential and the calculated planar average of the potential along the gap between the metallic thin films at equilibrium for the case of a Ti/Pt−Ti−Pt subsystem in contact with a Pt−Pt subsystem. Two regions with different electrostatic potential are formed, and at the interface, there is a potential barrier or built-in potential, in this case of 0.082 eV, calculated as the difference between the
Table 1. Amount of Electrons in the Gap (Defined in Figure 10) and Work Function for Various M/Pt Skin Systems metallic skinsurfaces
number of electrons in the gap (e)
work function of the composite system (eV)
Cu/Pt Ag/Pt Au/Pt Ni/Pt Pd/Pt Pt Co/Pt Rh/Pt Ir/Pt Fe/Pt Ru/Pt Os/Pt Tc/Pt Re/Pt W/Pt V/Pt Ta/Pt Ti/Pt
0.18 0.22 0.21 0.19 0.20 0.22 0.23 0.24 0.27 0.26 0.30 0.33 0.38 0.40 0.48 0.41 0.57 0.49
4.71 4.74 5.33 4.83 5.21 5.71 4.66 5.17 5.65 4.45 5.22 5.55 5.26 5.47 5.45 4.49 5.10 4.37
In the context of the periodic dependence of the results, it appears reasonable to expect a correlation between the amount of electrons in the gap and the electronegativity of the overlayer atoms. That is, a correlation may exist between the number of electrons that migrate from the surface to fill the gap and a chemical property that describes the tendency of an atom to attract electrons. Accordingly, it would be expected that the higher the electronegativity, the smaller the number of electrons in the gap. In fact, for a given period of the periodic table, as the atomic number Z increases, the electronegativity increases, whereas the amount of electrons in the gap decreases.
Figure 4. Top: Amount of electrons in the gap of skin−surface systems organized by location (period) of surface atoms in the periodic table versus surface oxidation charges (in e) due to the interaction of surface metal atoms with Pt atoms in the subsurface. Bottom: Correlation of the work function of the skin−surface systems with surface oxidation charges (in e). The blue line represents the amount of electrons in the gap and the work function of pure Pt. It is observed that is possible to increase or decrease the amount of electrons in the gap changing the overlayer metal, whereas for all skin surfaces, the work function decreases with respect to pure Pt. 821
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Figure 5. Electrostatic potential (in eV, see Figure 10) along the gap defined by merging a Ti/Pt−TiPt subsystem with an equivalent subsystem made of pure Pt; the separation between the metallic thin films is 5 Å. Two regions with different electrostatic potential are clearly identified.
Table 2. Built-In Potential, Work Function of the System, and Charge Gained by Pt Atoms at the Interface for Various Metal Skin−Surfaces
Figure 6. Electrostatic potential along the gap between metallic thin films and average electrostatic potential calculated along the gap defined in Figure 10 for the Ti/Pt skin surface system in contact with pure Pt. A built-in potential of 0.082 eV was calculated as the difference between the average potential along the gap in the region of pure Pt surfaces and the average potential along the gap in the region of Ti/Pt surfaces.
metallic skinsurfaces
built-in potential (eV)
work function of the system (eV)
charge gained by each Pt atom at the interface (ΔQ, in e)
Cu/Pt Ag/Pt Au/Pt Ni/Pt Pd/Pt Pt Co/Pt Rh/Pt Ir/Pt Fe/Pt Ru/Pt Os/Pt Tc/Pt Re/Pt W/Pt V/Pt Ta/Pt Ti/Pt
0.053 0.062 0.028 0.042 0.028 0 0.051 0.028 0.0071 0.062 0.031 0.014 0.032 0.020 0.033 0.061 0.051 0.082
5.27 5.19 5.55 5.35 5.47 5.71 5.24 5.49 5.69 5.13 5.49 5.63 5.46 5.58 5.51 5.12 5.29 4.92
0.14 0.12 0.12 0.15 0.083 0.05 0.18 0.094 0.081 0.23 0.13 0.13 0.19 0.20 0.30 0.33 0.40 0.43
surface atom reduction at junction). It is found that both properties (built-in potential and work function) decrease in a given period as the atomic number, Z, decreases. The tendencies of both values with respect to the location in the periodic table are similar since the built-in potential in the gap is related to the charge transferred at the interface. Comparing both results in Figure 7, it is concluded that the built-in potential in the gap between films increases as the work function of the system decreases. As in the case of Figure 4, the exceptions of the general trends are the systems with overlayer metal Cu, Ag, and Au, whose outermost d orbital is full with its 10 electrons. Composite Ti/Pt−Pt System af ter Relaxation. In the previous analyses, the geometry of the system was fixed in order to elucidate the effect of the nature of the overlayer metal on a similar basis. In this section, we consider only one case (Ti/Pt− Ti/Pt in contact with Pt−Pt) and let the system relax.
average potential along the gap in the region of pure Pt surfaces and the average potential along the gap in the region of Ti/Pt surfaces. The built-in potential was calculated taking into account the definition of “gap” given in the Computational Methods section (Figure 10). The total volume of the gap used to calculate the built-in potential for all systems was 6.73 Å3. Table 2 lists the values of the built-in potential for several skin surfaces in contact with pure Pt, as well as the work function of the systems and the charge gained by the Pt atoms at the interface. The work function of the system varies with the type of skin-metal M between the corresponding values for Pt− Pt and M/Pt−M/Pt subsystems before contact. Similarly to the analysis in Figure 4, the built-in potential and the work function from Table 2 are rearranged in Figure 7 in search of a correlation with the transferred charge (extent of Pt 822
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Figure 7. Built-in potential and work function as a function of charge (in e) gained by Pt atoms at the interface (Pt surface atom reduction at the junction). The built-in potential in the gap between films increases, whereas the work function decreases as the Pt surface atom reduction at the junction increases.
In summary, thin metal films separated by a subnanometer gap exhibit a strong interaction, which leads to migration of electrons to the gap region. The electronic properties of such region may be tuned by changing the nature of the interacting surfaces, for example, through polarization induced by an overlayer over a core of a different metal. A composite system formed by connecting M/Pt−M/Pt and Pt−Pt interacting surfaces in series along the y direction, exhibits a nonuniform electronic distribution at the junction area. At equilibrium, the two regions have different electrostatic potentials, thus generating a potential barrier or built-in potential at the junction. The built-in potential in the gap between metallic thin films, located at the junction area, depends on the chemical nature of the overlayers forming the interface. The electron density, work function of the system, and potential barrier follow a trend that can be ordered according to the periodic table and correlated to properties such as electronegativity and the number of unpaired electrons in the most external orbitals. The electrostatic barrier formed at the interface between the M/Pt−M/Pt and Pt−Pt systems resembles a p−n junction and therefore opens a new opportunity as a building block for electronic applications. Further, we suggest that external stimuli such as incident light and/or the incorporation of the studied systems into electrochemical devices, for instance, as nanostructured electrodes, may lead to modification of optical and chemical properties that could be the basis for other applications in sensing, photocatalysis, and electrochemistry.
Depending on the initial separation between the thin films prior the relaxation, the relaxed system evolves to a different separation between films and charge transfer between atoms with respect to the fixed composite system studied before. Two initial separations between the thin films were studied: 5.0 Å and 5.5 Å. Figure 8 illustrates the systems after relaxation. It is observed that the interatomic separation as well as the separation between the thin films changed. The relaxed gap between the thin films in not homogeneous, and the Ti layer surface reduced the gap size with respect to that between Pt surfaces as shown in Figure 8. This is expected since, as shown before, the Ti overlayer that forms the gap induces migration of more electrons inside the gap than the pure Pt layers, causing a stronger interaction between the surfaces. In addition, Figure 8 shows surface deformation with elongations and reductions of atomic distances. Depending on the degree of deformation that results after relaxation, the atomic charge distribution changes with respect to that in a fixed system. For the two cases studied, the system with an initial separation between thin films of 5.0 Å (Figure 8, bottom) is the most deformed, and exhibits more changes in the atomic charge distribution in comparison with the fixed system. This is illustrated in Figure 8 (bottom) and Figure 9 (bottom), showing the close proximity of the Ti surface layers from the two thin films in comparison with that in the gap between Pt surface layers (3.32 Å and 5.03 Å, respectively). The surface deformation increases the gradient of density of electrons in both regions of the system in comparison with the fixed system. This phenomenon in addition to the change in charge distribution on the atoms located in the junction shown in Figure 9 (bottom), causes an increase in the built-in potential formed in the gap between the thin films of this system in comparison with that calculated in the fixed system: 0.19 and 0.082 eV, respectively.
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COMPUTATIONAL METHODS DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP).19−22 Electron-ion interactions are described using the projector-augmented wave (PAW) method,23 expanded within a plane wave basis setting up a cutoff energy of 350 eV. Electron exchange and correlation 823
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Figure 9. Charge gained and lost after relaxation by atoms forming the surface and subsurface of the systems illustrated in Figure 8. Top: The initial separation between thin films prior to relaxation is 5.5 Å. Almost negligible changes in the charge distribution are found in comparison with the fixed system studied before. The built in potential of this system is the same as the fixed one reported before, 0.082 eV. Bottom: The initial separation between thin films prior to relaxation is 5.0 Å. Considerable surface deformation is reflected in changes in the charge distribution and built-in potential with respect to the fixed system reported before, 0.19 eV. We note that our study is exclusively based on DFT. Even though general inferences can be established, details of the analysis may depend on the type of exchange-correlation functional used for the calculations.18 Moreover, given the nature of the proposed system where electron correlation effects can be important, our conclusions should be revisited using higher order ab initio methods.
assumption that they represent a “bulk”. After relaxation, the resultant atomic positions were fixed, and the slab models were simulated at a slab separation of 5 Å to allow interaction between surfaces. Under these conditions and slab separation, the charge transfer at the interface and the charge in the gap between slabs were calculated. Additionally, two Ti/Pt−Pt systems were simulated, allowing all atoms to relax, one system with initial separation between thin films of 5.0 Å, and the other with 5.5 Å. In order to calculate the amount of electrons in the gap between the slabs and the built-in potential along the gap between the slabs, it is necessary to define the limits of the gap. Figure 10 shows the average potential along the direction perpendicular to the surfaces in the slab (direction z). The gap between slabs is defined starting at a distance 0.5 Å down from the center of the gap between thin films and ending 0.5 Å up from the same center. The total gap distance along the z direction is always 1 Å. In order to correctly represent the vacuum potential, the reported work function values were calculated when the separation between the thin films was 12 Å. The optimum bulk lattice constant of Pt was determined as 3.98 Å, a value 1.45% higher than the experimental (3.92 Å).25 Brillouin zone integration for the surface system was performed using a Monkhorst Pack grid26 of 9 × 9 × 1 for the case of 2 × 2 supercells and 8 × 2 × 1 for the case of 2 × 8 supercells, and a Methfessel-Paxton27 smearing of 0.2 eV. The convergence criteria for the electronic self-consistent iteration loop were set to 10−4 eV and the forces were converged to 0.01 eV/Å. The total electronic charge of an atom was calculated using Bader analysis.28,29 This analysis defines an atom based on the electronic charge density using zero flux surfaces to divide atoms; the total electronic charge of an atom is approximately
Figure 8. Composite Ti/Pt −Pt slab systems after relaxation. It is observed that the Ti surface layers reduced the size gap in comparison with the pure Pt surfaces, and considerable deformation is found in comparison with the fixed systems studied before. Top: The initial separation between thin films prior relaxation is 5.5 Å. Bottom: The initial separation between thin films prior to relaxation is 5.0 Å.
effects were described by the Perdew−Burke−Ernzerhof (PBE)24 generalized gradient approximation (GGA)-type exchange correlation functional. Spin polarization was included in every simulation. Two different systems were studied; both are represented as slab models infinite in the x and y directions and finite in the z direction (Figure 1). One system consists of a periodically repeated face-centered cubic (fcc) Pt slab covered by a monolayer of a metal M, (M = Ti, V, Fe, Co, Ni, Cu, Tc, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, Pt, and Au); the system was modeled using six layers in 2 × 2 supercells. The other system consists of a periodically repeated fcc Pt slab where half of the system is covered by a monolayer of the same metals described before and the other half is pure Pt. This system was modeled using seven layers in 2 × 8 supercells. Because of the periodic boundary conditions used in the three spatial directions, the top (111) surface is separated a distance H from another (111) surface, with the bottom layer of the slab in the top neighboring cell defining the gap. For both kinds of systems at H = 12 Å, a group of top and bottom layers were allowed to relax, whereas two central layers for the case of 2 × 2 supercells and three central layers for the case of 2 × 8 supercells were fixed, on the 824
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Figure 10. Average potential along the direction perpendicular to the surfaces. The gap between slabs is defined starting at a distance 0.5 Å down from the center of the gap between thin films and ending 0.5 Å up from the same center. The total gap distance along the z direction is always 1 Å.
the charge enclosed within the Bader volume defined by zero flux surfaces.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address
́ Departamento de Ingenieriá Quimica, Universidad Industrial de Santander, Bucaramanga, Colombia. †
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the Department of Energy, Grant DE-FG02-05ER15729. Computational resources from the Texas A&M University Supercomputer Center, from the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0376SF00098, and from the University of Texas at Austin TACC system are gratefully acknowledged.
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REFERENCES
(1) Ramirez-Caballero, G. E.; Balbuena, P. B. Effect of Confinement on Oxygen Adsorbed between Pt(111) Surfaces. J. Phys. Chem. C 2009, 113, 7851−7856. (2) Ramirez-Caballero, G. E.; Balbuena, P. B. Confinement Effects on Alloy Reactivity. Phys. Chem. Chem. Phys. 2010, 12, 12466−12471. (3) Ramirez-Caballero, G. E.; Mathkari, A.; Balbuena, P. B. Confinement-Induced Polymerization of Ethylene. J. Phys. Chem. C 2011, 115, 2134−2139. (4) Ramirez-Caballero, G. E.; Balbuena, P. B. Confinement-Induced Changes in Magnetic Behavior of a Ti Monolayer on Pt. Chem. Phys. Lett. 2010, 507, 117−121. (5) Martinez de la Hoz, J. M.; Balbuena, P. B. Geometric and Electronic Confinement Effects on Catalysis. J. Phys. Chem. C 2011, 115, 21324−21333. 825
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